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Solution of nonlinear degenerate elliptic-parabolic systems in Orlicz- Sobolev spaces. (English) Zbl 0722.35048
Differential equations and their applications, Proc. 7th Conf., Equadiff 7, Prague/Czech. 1989, Teubner-Texte Math. 118, 175-179 (1990).
[For the entire collection see Zbl 0704.00019.]
A double nonlinear parabolic system of the form $\partial_ tb(u)- \nabla a(t,x,\nabla u)=f(t,x,b(u))$ with a mixed (Dirichlet-Neumann) nonlinear boundary condition is considered where b is a gradient of $$C^ 1$$-convex function and a is monotone and coercive in $$\nabla u$$. An existence of a variational solution is proved, generally, in nonreflexive functional spaces of Orlicz-Sobolev type.
Reviewer: J.Kačur

MSC:
 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35M10 PDEs of mixed type 35D05 Existence of generalized solutions of PDE (MSC2000)
Keywords:
spaces of Orlicz-Sobolev type
Zbl 0704.00019